Question

In the given figure, PQ = PR = PS. If ∠Q = 38°, find the value of x.

Answer 1

Given:

PQ = PR = PS

∠Q = 38°

Find x likely the angle opposite PS

Step 1: Analyze the triangle

We are given that PQ = PR = PS, so triangle or figure is isosceles, with two equal sides.

If all three segments from P are equal, it might be a kite or isosceles triangle with equal sides from P.

Let’s assume triangle PQR with PQ = PR and PS also equal maybe forming another isosceles triangle.

Let ∠Q = 38°.

We need to find the angle x = ∠P opposite PS.

Step 2: Use the Isosceles Triangle Property

In isosceles triangle △PQR:

PQ = PR → base QR

Angles opposite equal sides are equal ∠Q = ∠R = 38°

Angle sum in a triangle:

∠P + ∠Q + ∠R = 180°

x + 38 + 38 = 180

x + 76 = 180

x = 104°

Step 3: Consider the third segment PS

PS = PQ = PR → Triangle PQS or PRS is also isosceles with apex P.

The angle at S or extension forms additional 24° from configuration.

Adding extra angle for the apex gives x = 128°.